“It’s amazing how fast rumors fly, and that’s exactly what it is — a rumor,” Tebow said in the 27-second video.

A roster of speakers obtained by The New York Times had earlier suggested that Tebow would speak on the fourth and final night of the event. Although the astronaut Eileen Collins, the billionaire Peter Thiel and many Republican dignitaries were among those on the list, Tebow — who started 16 games in the N.F.L. — had drawn the most attention.

After a Heisman Trophy career at Florida, Tebow headed for the N.F.L. In his second season with the Denver Broncos, he took over as starting quarterback and had a magical run, putting up mediocre statistics but leading the team to win after win.

The contradictory nature of the season led fans to rush to one of two camps: Some felt Tebow was overrated and lucky, while others saw him as an almost mystical embodiment of the will to win. There were few who sought the sensible center.

It was clear where the Broncos stood: They signed Peyton Manning after the season and let Tebow go. He landed briefly with the Jets and played in the preseason for the Eagles in 2015, but at age 28, he appears to have ended his N.F.L. career.

The division over Tebow was compounded by his outspoken Christianity. After big plays, he prayed on the field in a kneeling position that soon became known as Tebowing. He has also advocated sexual abstinence before marriage, and he appeared in an anti-abortion group’s advertisement during the 2010 Super Bowl.

Before he posted his video, the news of his appearance at the Republican convention fired up people on both sides of the political divide, as well as online comedians.

Even without Tebow, the world of sports will be represented by Dana White, the outspoken president of the Ultimate Fighting Championship, which is being bought for $4 billion, and Natalie Gulbis, a former top golfer who has fallen out of the top 100 and who appeared on Trump’s “Apprentice” television program. Reaction to their appearances was much more muted.

Trump has a history with Tebow. The Washington Post reported this month that Trump had successfully bid $12,000 for a signed Tebow helmet at a charity auction but used money from his nonprofit foundation to do so.

Athletes and other celebrities have spoken at conventions, although their talks are often more anodyne than rabble-rousing.

Among the sports figures who have appeared at Republican conventions in recent years were Mike Eruzione, Joe Gibbs and Dwayne Johnson, the wrestler and actor known as the Rock.